Farooqui has been accused of raping a 35-year-old American national.
"A 35-year-old American national woman was raped by the co-director of the film 'Peepli Live'. The incident took place on March 28, 2015, and a report in this connection was registered with the New Friends Colony police on June 19, 2015," a Delhi Police official told IANS.
"The accused Mahmood Farooqui has been arrested and was presented before Saket court. The court has sent him into judicial custody till July 6," added the official.
The victim is pursuing Ph.D. from Columbia University and was in India for some research work.
When IANS tried to contact Farooqui's wife and director-screenwriter Anusha Rizvi, she remained unavailable for a comment.
Rizvi and Farooqui co-directed the 2010 satirical comedy film "Peepli Live", produced by Bollywood superstar Aamir Khan.